The invention disclosed and claimed herein generally pertains to phase and phase difference magnetic resonance (MR) imaging. More particularly, the invention pertains to a method for correcting the effect of distortion in a set of MR data to be used in phase or phase difference imaging, wherein the distortion results from non-linearity in one or more gradient magnetic fields used in acquiring the data.
As is well known, acquired MR imaging data can be represented in quadrature. That is, the MR signal at each pixel location can be represented by two complex components which are 90 degrees out of phase, commonly referred to as the I and Q components, respectively. Thus, the MR signal at each pixel location has a magnitude equal to .sqroot.(I.sup.2 +Q.sup.2), and a phase component equal to the arctangent of (Q/I), or tan.sup.-1 (Q/I).
In the past, it has been most common to employ signal magnitude in forming MR images. However, it is now recognized that for certain applications, such as imaging of flowing fluids (such as blood or cerebral spinal fluid) and shimming, there are distinct benefits in using the phase component at respective pixel locations to form MR phase and phase difference images. As is known by those of skill in the art, a phase difference image can be constructed by first obtaining two phase images of a subject. An imaging parameter is varied between the two phase images, so that the respective phases thereof are different. For example, in phase contrast angiography, also known as phase mapping, wherein flow velocity along an axis is to be measured, the value of the first gradient moment along the axis is varied to produce two different data sets. One of the phase images is then subtracted from the other, on a pixel-by-pixel basis, to provide the phase difference image. Thus, given two phase images .phi..sub.A =tan.sup.-1 (Q.sub.A /I.sub.A) and .phi..sub.B =tan.sup.-1 (Q.sub.B /I.sub.B), the phase difference .DELTA..phi. may be obtained from subtraction, i.e., .DELTA..phi.=.phi..sub.B -.phi..sub.A. As known to those skilled in the art, the phase difference is more commonly calculated with a single arctangent via the expression: EQU .DELTA..phi.=tan.sup.-1 {(I.sub.A Q.sub.B -I.sub.B Q.sub.A)/(I.sub.A I.sub.B +Q.sub.B Q.sub.A)} Equation 1
The single arctangent function ensures .DELTA..phi. in Equation 1 covers a range of 2.pi. radians or 360 degrees. The invention herein and the teachings set forth with respect thereto are considered to apply to both phase images and phase difference images. Hereinafter, the term "phase information image" is used to refer to both phase and phase difference images.
As is further well known, a set of MR image data may be acquired under conditions wherein the X-, Y- and/or Z- gradient magnetic fields are non-linear relative to their respective axes, across at least a portion of the field of view. Imperfect linearity, or nonuniformity, of the gradient, which results in image distortion, is of particular concern if the field of view is comparatively large, which often is the case, for example, for imaging the spine in the sagittal plane. Accordingly, techniques have been developed to geometrically correct an image for the distorting effects of gradient nonuniformity, as exemplified by commonly assigned U.S. Pat. No. 4,591,789, issued May 27, 1986 to Glover and Pelc. Such patent is directed to a technique hereinafter referred to as "Gradwarp".
The Gradwarp technique applies a two step process to a set of MR data elements, wherein the elements comprise nominal values of an MR signal parameter at respective locations in a set of pixel locations. In accordance with the first step, a magnification/minification, pixel displacement or warp factor, which is determined by the gradient nonuniformity, is applied to displace or remap respective data elements to their actual locations. In the second step, an interpolation is performed, using the displaced data elements, to determine the actual or corrected values of the MR signal parameter at respective pixel locations. The interpolation step commonly uses polynomial interpolation, such as a cubic or quartic function, such as fitting a cubic spline curve through four displaced data elements close to a pixel location, and then sampling the curve at the pixel location.
Techniques such as Gradwarp have generally been quite effective in correcting distortion of the above type in images constructed from MR signal magnitudes. However, if the Gradwarp technique is applied to the respective phase values of a phase image, the corrected phase image, or phase map, will not be unwrap-compatible. Unwrap-compatibility is discussed in more detail hereinafter, in connection with FIG. 2 of the drawings. In addition, overshoot and ringing, also described hereinafter, can occur in applying the interpolation step to compute corrected phase values at pixel locations which are close to a boundary or interface between materials of very different MR properties, such as body tissue and air. Overshoot causes artifacts in the form of bright and dark spots which lie along the boundary.